Can TIFFs be exported in CMYK?

EPS files use the PostScript page description language to describe vector and raster objects. PostScript is the publishing industry standard for high-end graphics files, cartography, and printing. EPS files can be edited in many drawing applications or placed as a graphic in most page layout applications. EPS files exported from ArcMap support embedding of fonts so that users who do not have Esri fonts installed can still view the proper symbology. EPS exports from ArcMap can define colors in CMYK or RGB values.

TIFF (Tagged Image File Format)

TIFF files are the best choice for importing into image editing applications and are also a common GIS raster data format. However, they cannot be natively viewed by a web browser. ArcMap TIFFs exported from the data view also support georeferencing information in GeoTIFF tags or in a separate world file for use as raster data.

Can ArcMap Documents be exported as TIFFs from ArcMap and define colors in CMYK values?

Short answer is no it can't—if needed I usually go to PDF and then rasterize that using Photoshop. Keep in mind Arc's RGB to CMYK conversion is not great and has no knowledge of colour profiles so make sure colours are spec'd in the colour space you plan to export to.

Having said that I think PLTS/Production Mapping extension does allow for setting up of CMYK and Spot separations as TIF files but that's a whole other topic and one I couldn't help with...

Short answer is no it can't—if needed I usually go to PDF and then rasterize that using Photoshop. Keep in mind Arc's RGB to CMYK conversion is not great and has no knowledge of colour profiles so make sure colours are spec'd in the colour space you plan to export to.

Having said that I think PLTS/Production Mapping extension does allow for setting up of CMYK and Spot separations as TIF files but that's a whole other topic and one I couldn't help with...